Advanced Virgo - Advanced Virgo sensitivity curve study VIR-0073D-12 Authors: M Punturo1 Issue: D Date: November 19, 2012 1 INFN - Sezione di Perugia, Italy, AdV { Advanced Virgo { Sensitivity Curve Study Web: https://wwwcascina.virgo.infn.it/ Email: [email protected] VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 2 of 78 Abstract This document describes the sensitivity curve modeling of the Advanced Virgo detector. Table 1: Document history Issue Date Description A 09-03-2012 First description of the fundamental noises, as currently implemented in gwinc. Just started the computation of the AdV noise and missing any evaluation of technical noises (to be inserted in a future release). B 29-03-2012 Residual seismic noise introduced in gwinc and in the note. Losses bud- get introduced in the quantum noise chapter C 24-07-2012 Detection distance corrected by Patrick Sutton, because of an incorrect integration constant, resulting in to an increment of about 6% in the horizon (function int73.m). Reference configuration file modified reduc- ing the clear aperture for the clipping losses to 33 cm dominated by the baffles and not by the coating. Suspension thermal noise still to be modified because computed taking in account a reference mass anymore present in the AdV design. D 19-11-2012 Thermal noise model updated removing the reference mass. VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 3 of 78 Contents 1 Seismic Noise 5 1.1 The Virgo seismic filtering system . .5 1.2 Gravity Gradient Noise . .6 2 Test mass Thermal Noises 11 2.1 Mirror Brownian Noise . 11 2.1.1 The coating contribution . 12 2.1.2 Substrate loss angle . 12 2.1.3 Surface losses contribution . 13 2.2 Substrate thermo-elastic noise . 13 2.3 Thermo-optical noises . 14 3 Suspension Thermal Noise 17 3.1 Including the violin modes of the mirror suspension wires . 18 3.1.1 Optimized (Dumbbell{shaped) fibres . 19 3.2 Vertical bouncing mode thermal noise . 19 4 Residual Gas 20 5 Quantum Noise 20 5.1 Initial interferometers . 20 5.2 Read{out schemes . 21 5.3 Signal Recycled interferometer . 21 5.4 Optical losses budget . 24 6 AdV Sensitivity 26 Bibliography 27 Nomenclature 30 Appendices 32 A IFO structure 32 B Brownian Substrate Code 41 C Seismic noise generation Code 42 D Brownian Substrate Finite Size Correction Code 43 E Brownian Coating parameters feeding Code 45 F Brownian Coating Code 47 G Thermo-elastic Substrate Code 50 H Thermo-elastic Substrate Finite Correction Code 51 I Thermo-optical coating core computation Code 52 J Thermo-optical coating core computation Code 55 K Thermo-elastic Coating Finite Correction Code 57 VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 4 of 78 L Suspension Thermal Noise Code 60 M Optimised fibre Code 67 N Residual Gas Code 71 O Quantum (optical read{out) noise 73 P Miscellanea of computations 76 VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 5 of 78 1 Seismic Noise The seismic noise, consisting in to the natural and anthropogenic shaking of soil, enters in the noise budget of AdV through both the residual vibration transmitted through the SA to the mirrors and the direct coupling due to the Newtonian attraction force of the suspended test masses to the soil (the so{called Newtonian or Gravity Gradient Noise [1{3]). Seismic activity at the Virgo site is obviously affected by the weather conditions (wind, sea excitation) and by the human activity (for few examples see [4] and [5]). In particular, at the Virgo site, the wind effect is visible under 0:1 Hz, the ocean between 0:1 and 0:2 Hz, the Tirreno sea between 0:2 and 1 Hz, the traffic between 1 and 5 Hz [6]; this generate a structured noise, mainly below the detection cut{in frequency. This noise (so called µ{seism) obviously fluctuates according to the environmental condition, as shown in Fig.1 and in Fig.2. Figure 1: Spectral amplitude of the (µ{) seismic displacement noise measured in the Virgo Central Building (CB). The color level indicates the persistence of the noise amplitude in the correspondent range [7]. An accurate simulation of the seismic noise should take in account all these structures; this has been attempted trying to reproduce the main bumps at low frequency and the ≈ 10−7=f 2 behavior at high frequency pj Y 2 2 fjf X xseism = a1 · f − f + i + a2 · bumps (1) j Q j=1;3 j Bump functions are coded inside groundSeism.m (see Appendix C). In gwinc these parameters are contained in ifo.Seismic. In Fig.3 the seismic noise measured in the Virgo CB is compared with the model of Eq.1 in case of quiet µ{seism. In Fig.4 the same comparison is made in case of noisy environmental conditions. 1.1 The Virgo seismic filtering system The most recent description of the filtering performance of the Virgo Super{Attenuator (SA) is in [8]. Essentially some reduction of the filtering capability has been seen, probably due to a magnetic short{cut in the vertical VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 6 of 78 Figure 2: Statistical property of the spectral amplitude of the (µ{) seismic displacement noise measured in the Virgo Central Building (CB). For each frequency bin, it is reconstructed the probability to find a seismic amplitude below the threshold indicated by each curve [7]. chain of filters, but it is still valid to approximate the transfer function (TF) of the whole chain, by the product of the TFs of each stage. A detailed description of the SA TF computation is in the Paolo Ruggi Thesis [9] and here only the results are reported. In Fig.5 the Horizontal and Vertical TFs are shown [6]. The Blue curve represents the TF from the filter 0 to the mirror for the horizontal displacement; the determine the effective filtering the inverted pendulum filtering should be considered. For technical reason, it is preferred to measure the seismic noise on the top of the IP and to consider the filtering properties of the chain F0{mirror. The Red curve represents the Vertical TF ground{to{mirror. It is clear that in the in{band frequency range, the role of the vertical{to{horizontal coupling is crucial to determine the effective filtering of the SA. A mechanical −3 coupling angle of about θc ' 10 is expected. Adopting such as coupling angle it is possible to compute the residual seismic noise at the level of the mirror, as shown in Fig.6. 1.2 Gravity Gradient Noise The Gravity gradient noise or Newtonian Noise [1{3] is due to the direct coupling, through the Newtonian attraction force, of the suspended test masses to the soil. The latest and more general evaluation of this noise source has been done by G. Cella in [10] (see Eq.50 in [10]); for low frequencies and surfacep detector that evaluation coincides with the previous estimation [2] of the spectral amplitude (in terms of h 1= Hz): p 2 π 4π ! 2 h (!) = GG · x (!); ! = pGρ (2) GGN 3 L ! seism GG soil where G is the (universal) gravity constant and ρsoil is the averaged density of the soil in the AdV site (ρ ' 2300 − 2700 [kg=m3] [11, 12]). VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 7 of 78 Virgo central building, quiet condition (1am and calm sea) −5 10 VERTICAL Virgo EW Virgo NS −6 10 model 2e−7/f2 AdV model −7 10 −8 10 −9 m / sqrt(Hz) 10 −10 10 −11 10 −12 10 −1 0 1 2 10 10 10 10 Hz Figure 3: Seismic noise in the Virgo CB [7], in a condition of quiet µ{seism. The green curve shows the spectral amplitude of the vertical seismic red curve the East{West horizontal vibration and the blue curve the North{South horizontal seismic vibration. The dashed black line is the 10−7=f 2 simple model. The magenta markers shows the prediction of Eq.1, computed with the low noise parameters. VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 8 of 78 Virgo central building, noisy condition (8am, high microseism) −5 10 VERTICAL Virgo EW −6 Virgo NS 10 model 2e−7/f2 AdV model −7 10 −8 10 −9 m / sqrt(Hz) 10 −10 10 −11 10 −12 10 −1 0 1 2 10 10 10 10 Hz Figure 4: Seismic noise in the Virgo CB [7], in a condition of noisy µ{seism. The green curve shows the spectral amplitude of the vertical seismic red curve the East{West horizontal vibration and the blue curve the North{South horizontal seismic vibration. The dashed black line is the 10−7=f 2 simple model. The magenta markers shows the prediction of Eq.1, computed with the high noise parameters. VIR-0073D-12 issue :D AdV sensitivity date : November 19, 2012 page : 9 of 78 5 10 Horizontal TF Vertical TF 0 10 −5 10 −10 Transfer Function 10 −15 10 −20 10 −2 −1 0 1 2 10 10 10 10 10 Hz Figure 5: Transfer Functions (TF) of the Virgo SA [6]: Blue curve, Horizontal TF from the filter 0 to the mirror. To determine the effective filtering the role of the inverted pendulum (IP) must be inserted. Red curve, Vertical transfer function from ground to mirror (in this plot two curves, relative to a different frequency sampling, have been overlapped).